LEADER 04869nam 22008173 450 001 9910960760203321 005 20231110232504.0 010 $a9781470469153 010 $a1470469154 035 $a(MiAaPQ)EBC6852911 035 $a(Au-PeEL)EBL6852911 035 $a(CKB)20667666500041 035 $a(RPAM)22491296 035 $a(OCoLC)1295277368 035 $a(EXLCZ)9920667666500041 100 $a20220117d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aElliptic Theory for Sets with Higher Co-Dimensional Boundaries 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$dİ2021. 215 $a1 online resource (136 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.274 300 $a"November 2021, volume 274." 311 08$aPrint version: David, Guy Elliptic Theory for Sets with Higher Co-Dimensional Boundaries Providence : American Mathematical Society,c2022 9781470450434 320 $aIncludes bibliographical references. 327 $aThe Harnack chain condition and the doubling property -- Traces -- Poincare? inequalities -- Completeness and density of smooth functions -- The chain rule and applications -- The extension operator -- Definition of solutions -- Harmonic measure -- Green functions -- The comparison principle. 330 $a"Many geometric and analytic properties of sets hinge on the properties of elliptic measure, notoriously missing for sets of higher co-dimension. The aim of this manuscript is to develop a version of elliptic theory, associated to a linear PDE, which ultimately yields a notion analogous to that of the harmonic measure, for sets of codimension higher than 1"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aDifferential equations, Elliptic 606 $aDegenerate differential equations 606 $aHarmonic functions 606 $aHarmonic analysis 606 $aBoundary value problems 606 $aPotential theory -- Higher-dimensional theory -- Harmonic, subharmonic, superharmonic functions$2msc 606 $aPartial differential equations -- Elliptic equations and systems -- Boundary value problems for second-order elliptic equations$2msc 606 $aMeasure and integration -- Classical measure theory -- Length, area, volume, other geometric measure theory$2msc 606 $aMeasure and integration -- Classical measure theory -- Hausdorff and packing measures$2msc 606 $aPartial differential equations -- Elliptic equations and systems -- Degenerate elliptic equations$2msc 606 $aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Caldero?n-Zygmund, etc.)$2msc 606 $aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory$2msc 606 $aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE$2msc 615 0$aDifferential equations, Elliptic. 615 0$aDegenerate differential equations. 615 0$aHarmonic functions. 615 0$aHarmonic analysis. 615 0$aBoundary value problems. 615 7$aPotential theory -- Higher-dimensional theory -- Harmonic, subharmonic, superharmonic functions. 615 7$aPartial differential equations -- Elliptic equations and systems -- Boundary value problems for second-order elliptic equations. 615 7$aMeasure and integration -- Classical measure theory -- Length, area, volume, other geometric measure theory. 615 7$aMeasure and integration -- Classical measure theory -- Hausdorff and packing measures. 615 7$aPartial differential equations -- Elliptic equations and systems -- Degenerate elliptic equations. 615 7$aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Caldero?n-Zygmund, etc.). 615 7$aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory. 615 7$aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE. 676 $a518/.64 686 $a31B05$a35J25$a28A75$a28A78$a35J70$a42B20$a42B25$a42B37$2msc 700 $aDavid$b Guy$0350534 701 $aFeneuil$b Joseph$01802032 701 $aMayboroda$b Svitlana$01802033 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910960760203321 996 $aElliptic Theory for Sets with Higher Co-Dimensional Boundaries$94347557 997 $aUNINA